Access Point #: MAFS.912.N-CN.1.AP.2bArchived Access Point

Essential Understandings

Concrete:

• Match i with the  .
  
  
• Match the parts of a complex number with a label.
  e.g., a + bi (a is the real part and bi is the imaginary part)
  i =  .
• Use manipulatives to represent terms for the purpose of simplifying and combining like terms.
• Use manipulatives to combine like terms (i.e., demonstrate 5i + 3i by combining like manipulatives).
• Create an array of objects for the mathematical equation and match the answer symbol (+ or -) following addition/subtraction rules for an equation.
• Create an array of objects for the mathematical equation and match the sign positive or negative following multiplication rules for an equation. 
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• Understand the following concepts, symbols, and vocabulary for: like terms, combine, variables, positive integer, negative integer, real number, imaginary number, complex number, squares, square roots.
• Understand that i in its simplified form changes its sign based on its exponent. For example:
  
• Use tools, as needed, to multiply two complex numbers.
  For example:
  Reminder: i²  = -1
  (a + bi)(c + di) = ac + adi + bci + bdi²
  
  (2 + 3i)(1 + 2i) = 2 + 4i + 3i + 6i² 
  
  2 + 7i – 6 = -4 + 7i